Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T21:50:16.650375Z
Paper Citation Record · LEDGER
As of 13 August 2026, this Paper Citation Record lists 50 of 50 outbound references and 0 inbound Pith citation observations for arXiv:2506.23438.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T21:50:16.650375Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
50 of 50 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 634ed928-349e-40fa-8f74-605a1217fbb8 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Aggarwal, Y
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 844cbf03-ee1b-42f2-b80b-063881f3c2ee · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Ajtai, The shortest vector problem in L2 is NP-hard for randomized reductions
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 53f4b365-7202-4ff4-a7f4-567f29e87f48 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Ajtai, Generating hard instances of lattice problems
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 4d5d20ea-ef68-4009-b3bb-f4c336d9daa2 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Ajtai and C
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation ef568a0d-f1a4-41e1-9c2b-5e69e02f6529 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography A Survey on Post-Quantum Cryptography: State-of-the-Art and Challenges
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 3174028b-a7a8-4754-a05e-c459f3d7a4e5 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Babai, On Lov´ asz’ lattice reduction and the nearest lattice point problem
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 82e354c5-bd27-4052-b15a-14a0ee7616d1 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Unresolved cited work
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 258608df-42bd-4a34-bc0e-1c420613e0f1 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Unresolved cited work
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation b9e484bd-2533-42cf-bdbd-0d935d978d48 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Deutsch and R
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation d6d20e01-7f1b-4e8a-a315-250f7b5efa43 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Diffie and M
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 0ff581db-0eb2-45d9-a5eb-265ec8afa12f · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Dinur, G
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 66a7079b-3f96-4d89-869d-ed9d14316e15 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography ElGamal, A public key cryptosystem and a signature scheme based on discrete logarithms
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation db368c53-b5f3-4c89-a0a1-9dc716b7c28f · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Gentry, Fully homomorphic encryption using ideal lattices
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation a364beec-bf0c-4e90-be68-f511d6171cb1 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Goldreich, S
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 74fbaf08-8d4a-4883-a586-9fe0dd4d28e3 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Goldreich, D
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation a33e3996-c776-49ee-9592-b6a5677a13d1 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Goldwasser, Mathematical foundations of modern cryptography: computational complexity perspective
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 9e63a1ba-2ab9-47fd-bccf-05d3c7f5100d · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Hoffstein, J
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 71264e16-4eac-4d6d-a0e6-480f6897069a · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Hoffstein, J
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 125f2e3a-8b27-4ec6-97d5-7dd006059e76 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Kannan and L
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation fcc4c698-1127-4367-b9cf-9ae565e3bc02 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Khot, Hardness of approximating the shortest vector problem in lattices
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 97c4245d-f3bc-4767-badb-d7b207fad958 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Klartag, Lattice packing of spheres in high dimensions using a stochastically evolving ellipsoid, arXiv:2504.05042
Reference 21
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9665702a-8f67-483b-be00-719f072748eb · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Koblitz, Elliptic curve cryptosystems
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation e3591639-09b5-45d9-ae01-540303a51cc1 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Unresolved cited work
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 68ddf398-6ab3-4838-94f1-45105cc9e851 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography of Math.(2) 185 (2017), no
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 429289dd-8449-4aa5-89d0-f51948871e3a · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Unresolved cited work
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 4b35a03e-4968-4948-8415-1f2d3091c838 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Unresolved cited work
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 838fef99-e952-46b1-9cb2-52c667a4ffd7 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Micciancio, Almost perfect lattices, the covering radius problem, and applications to Ajtai’s connection factor, SIAM J
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation d611a91c-30ce-4909-8083-b7a841d8729a · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Micciancio and S
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 99c5411f-348a-46fb-8b9b-00ea8d45d685 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Micciancio and O
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation dcec256c-6527-4f46-a6ce-1fd7f7cb6ad3 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Unresolved cited work
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 9441d6f0-013f-4336-84f7-604b721fadc8 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Unresolved cited work
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation c8aef107-44b1-41de-b857-668606e130c6 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Ordentlich, O
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 9509a123-125a-46b7-953f-034038582e6f · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Peikert, A Decade of Lattice Cryptography, Found
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 9f5c365d-02ae-4fc0-ba4b-19244ebcfa42 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Proos and C
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 89c25852-d4d7-48fc-a8ac-2832659a5397 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Unresolved cited work
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 72b9e828-054b-4fb2-892e-37b9b0f326ee · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Regev, On lattices, learning with errors, random linear codes, and cryptography
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation a32188de-8e8e-4df6-88b7-dce1a5b70dd9 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Regev, An Efficient Quantum Factoring Algorithm, J
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 882eaf8f-028b-4bab-b6e3-ba295eed16d1 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Unresolved cited work
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation cd13d1cb-dd92-49d4-95a7-931928ec5d80 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Unresolved cited work
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 048254e6-59ae-4e24-a47d-30b2e4105d06 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Schnorr, A hierarchy of polynomial time lattice basis reduction algorithms
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation a514e199-9112-4243-9ff0-8a8e946a43c0 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Unresolved cited work
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 42d2c47e-df56-44a5-b57b-fd002ed5ef25 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography S¨ odergren, On the distribution of angles between the N shortest vectors in a random lattice,J
Reference 42
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 4b6e40b9-f36f-4ab9-b871-ce0fd95e75f2 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography van Emde Boas, Another NP-complete problem and the complexity of computing short vectors in a lattice
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 30ea6acf-0c5a-4788-8fc4-c571a62cf42e · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Viazovska, The sphere packing problem in dimension 8
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation a7bb96ae-764f-4fc2-b104-e5c571383447 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Unresolved cited work
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 6069ddf7-6a58-4fcc-8f42-40b1f0e278d2 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Zhang and Z
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation dd378f69-b89c-4811-8dcc-2d0a16c94456 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Zong, Sphere Packings, Springer-Verlag, New York, 1999
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 062dc9a4-c2e3-45d0-aa5f-960b1b864315 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Zong, From deep holes to free planes, Bull
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 348212ea-49f6-4dff-8e13-e5c4a698b426 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography Zong, Some mathematical mysteries in lattices (Abstract of a plenary talk), ASIACRYPT 2012, LNCS, 7658, 2-3
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation aa2f4688-2781-4d9a-98c0-90626336a786 · outbound
Some Mathematical Problems Behind Lattice-Based Cryptography The Mathematical Foundation of Post-Quantum Cryptography
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
No inbound Pith citation observations are available.